Isothermic constrained Willmore tori in 3-space
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DOI: 10.1007/s10455-021-09778-1
Abstract: We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below $$8\pi $$ 8 π . In particular, every constrained… read more here.
Keywords: tori space; geometry; isothermic constrained; willmore tori ... See more keywords
First explicit constrained Willmore minimizers of non-rectangular conformal class
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DOI: 10.1016/j.aim.2021.107804
Abstract: We study immersed tori in $3$-space minimizing the Willmore energy in their respective conformal class. Within the rectangular conformal classes $\;(0,b)\;$ with $\;b \sim 1\;$ the homogenous tori $\;f^b\;$ are known to be the unique… read more here.
Keywords: rectangular conformal; minimizers non; non rectangular; willmore minimizers ... See more keywords
Candidates for non-rectangular constrained Willmore minimizers
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DOI: 10.1016/j.geomphys.2021.104221
Abstract: For every $\;b \sim 1,$$b \neq1\;$ fixed, we explicitly construct a $1$-dimensional family of putative constrained Willmore minimizers parametrized by their conformal class $\;(a,b) \sim (0,1).\;$ Indeed we show in \cite{HelNdi1} that these candidates minimize… read more here.
Keywords: rectangular constrained; candidates non; non rectangular; willmore minimizers ... See more keywords